Since I am doing some work using intelligence test data, I wanted to read something introductory material on that topic. Enter Intelligence: A Very Short Introduction (2001) by Ian J. Deary. I found this a useful introduction to how psychologists/psychometricians have thought about these things. What I was really after was the foundational stuff in chapter 1, and that is what I will focus on here. (Though chapter 6 on the Flynn effect is also solid, and taught me that American SAT scores have been declining in the same period as IQ scores have been rising.)

Deary takes the test collection called Wechsler Adult Intelligence Scale III as a starting point. WAIS-III consists of 13 different tests, and strikingly,

“every single one of those 13 tests in the WAIS-III  has a positive correlation with every other one. People who are better at any one test tend to be better at all of the others. There are 78 correlations when we look at all the pairings among the 13 tests. Every single correlation is positive – a good score on one of the tests tends to bring with it a good score on the others. There are no tests unrelated to any other one, i.e. there are noe near-to-zero correlations. There are no tests that are negatively related with other ones. Even the lowest correlation between any two tests is still a modest 0.3 (between picture completion and digit span). […]

The first substantial fact, then, is that all of these different tests show positive associations – people good at one tend to be good at all of the others. […]

The second important fact is that some sub-groups of tests in the WAIS-III collection associate higher among themselves than with others. For example, the tests of vocabulary, information, similarities, and comprehension all have especially high associations with each other. So, although they relate quite strongly to every test in the WAIS-III collection, they form a little pool of tests that are especially highly related among themselves. The same thing occurs with digit span, arithmetic, and letter-number sequencing. They relate positively with all of the other tests in the collection, but they relate especially highly with each other (pp. 7-8).”

In the WAIS-II tests, there are four groups of tests that correlate particularly strongly (called “group factors”), labelled: Verbal comprehension, Perceptual organization, Working memory, and Processing speed, ref. the figure below (p. 3). 

Positive correlations between the four group factors are high. This has often been taken to imply that the skills required to do well on each have some common source, which has traditionally been called g (“general factor”). Strictly speaking, the fact that the different test scores are positively correlated does not imply that they have something in common or that “g” corresponds to anything real. Deary is at one point fairly clear about this, writing: “The rectangles in Figure 1 are actual mental tests – the 13 sub-tests – that make up the Wechsler collection. The four circles that represent the ‘group factors’ and the circle that contains g are optimal ways of representing the statistical associations among the tests contained in the rectangles. The things in the circles, the specific/group factor abilities and ‘g’, do not equate to things in the human mind – they are not bits of the brain (p. 11).”

Though he muddles it somewhat when continuing with “The names we pencil into the circles are our common-sense guesses about what seems to be common to the sub-groups of tests that associate closely. The circles themselves emerged from the statistical procedures and the data, not from intuition about the tests’ similarities, but the labels we give the circles have to be decided by common sense (p.11),” and later much more by going on to treat ‘g’ as a valid stand-alone explanatory concept, and writing e.g. “We already know from Chapter 1 that there is general ability and there are […] specific types of mental ability (p. 85).”

Nevertheless, the book seems to be a good exposition of intelligence testing and how psychologists have viewed and continue to view the results of these tests.